Genetic Polymorphism and Speciation- An Adaptive Dynamics Perspective -

Eva Kisdi & Stefan GeritzDept. of Mathematics, University of Turku

Evolutionary branching

Resource competition * Christiansen & Loeschcke 1980 * Abrams et al. 1993 * Doebeli 1996 * Metz et al. 1996 * Meszéna & Metz 1996 * Dieckmann & Doebeli 1999 * Day 2000 * Drossel & McKane 2000 * Day 2001 * Claessen & Dieckmann 2002 * Schreiber & Tobiason 2003 * Vukics et al. 2003

Asymmetric competition * Abrams et al. 1993 * Geritz et al. 1999 * Kisdi 1999 * Jansen & Mulder 1999 * Kisdi & Geritz 2001

Predation * Abrams et al. 1993 * Van der Laan & Hogeweg 1995 * Doebeli & Dieckmann 2000 * Day et al. 2002 * Bowers et al. 2003 * Dercole et al. 2003

Host-parasite systems * Boots & Haraguci 1999 * Koella & Doebeli 1999 * Regoes et al. 2000

Cannibalism * Dercole & Rinaldi 2002 * Dercole 2003 * Nishimura & Isoda 2004

Mutualism * Doebeli & Dieckmann 2000 * Law et al. 2001 * Ferdy et al. 2002 * Ferriere et al. 2002

Spatial heterogeneity * Brown & Pavlovic 1992 * Meszéna et al. 1997 * Geritz et al. 1998 * Kisdi & Geritz 1999 * Geritz & Kisdi 2000 * Kisdi 2001 * Mathias & Kisdi 2002 * Doebeli & Dieckmann 2003 * Mizera & Meszéna 2003 * Egas et al. 2004

Temporal fluctuations * Kisdi in prep.

Metapopulations * Cohen & Levin 1991 * Doebeli & Ruxton 1997 * Parvinen 1999 * Mathias et al. 2001 * Kisdi 2002 * Parvinen 2002

Mating systems * Hoekstra 1980 * Metz et al. 1992 * Cheptou & Mathias 2001 * De Jong & Geritz 2001 * Maire et al. 2001 * Van Dooren & Leimar 2003

Sexual selection * Van Doorn & Weissing 2001 * Van Doorn et al. 2001

Microbial metabolism * Doebeli 2002 * Friesen et al. 2004

Prebiotic replicators * Meszéna & Szathmáry 2001

Resource competition * Christiansen & Loeschcke 1980 * Abrams et al. 1993 * Doebeli 1996 * Metz et al. 1996 * Meszéna & Metz 1996 * Dieckmann & Doebeli 1999 * Day 2000 * Drossel & McKane 2000 * Day 2001 * Claessen & Dieckmann 2002 * Schreiber & Tobiason 2003 * Vukics et al. 2003

Asymmetric competition * Abrams et al. 1993 * Geritz et al. 1999 * Kisdi 1999 * Jansen & Mulder 1999 * Kisdi & Geritz 2001

Predation * Abrams et al. 1993 * Van der Laan & Hogeweg 1995 * Doebeli & Dieckmann 2000 * Day et al. 2002 * Bowers et al. 2003 * Dercole et al. 2003

Host-parasite systems * Boots & Haraguci 1999 * Koella & Doebeli 1999 * Regoes et al. 2000

Cannibalism * Dercole & Rinaldi 2002 * Dercole 2003 * Nishimura & Isoda 2004

Mutualism * Doebeli & Dieckmann 2000 * Law et al. 2001 * Ferdy et al. 2002 * Ferriere et al. 2002

Spatial heterogeneity * Brown & Pavlovic 1992 * Meszéna et al. 1997 * Geritz et al. 1998 * Kisdi & Geritz 1999 * Geritz & Kisdi 2000 * Kisdi 2001 * Mathias & Kisdi 2002 * Doebeli & Dieckmann 2003 * Mizera & Meszéna 2003 * Egas et al. 2004

Temporal fluctuations * Kisdi in prep.

Metapopulations * Cohen & Levin 1991 * Doebeli & Ruxton 1997 * Parvinen 1999 * Mathias et al. 2001 * Kisdi 2002 * Parvinen 2002

Mating systems * Hoekstra 1980 * Metz et al. 1992 * Cheptou & Mathias 2001 * De Jong & Geritz 2001 * Maire et al. 2001 * Van Dooren & Leimar 2003

Sexual selection * Van Doorn & Weissing 2001 * Van Doorn et al. 2001

Microbial metabolism * Doebeli 2002 * Friesen et al. 2004

Prebiotic replicators * Meszéna & Szathmáry 2001

http://users.utu.fi/evakis/addyn.htm

• random dispersal to two habitats

• within-habitat selection:

• within-habitat competition: fixed number of adults emerge

• random mating in the entire population

A1A1 A1A2 A2A2

Habitat 1 f11 f12 f13 Habitat 2 f21 f22 f23

f1i f2i

c1 c2

offspring

adults

Levene's Soft Selection Model

Continuum of Alleles, Small Mutations

phenotype (x)

f1(x) f2(x)d

fitne

ss

with

in h

abita

t

f1(x) f2(x)

c1 c2

offspring

adults

(1) Clonal (haploid) inheritance(2) Diploid, 1 locus with additive allelic effects on the phenotype(3) Diploid with assortative mating

d/=3, c1=0.5

+

+

-

-

x1

x2

d/

Clonal model

Evolutionary branching of phenotypes

0

0.5

1

1 2 3 4d/

c1

Clonal model: evolutionary branching of phenotypesDiploid 1-locus model: evolutionary branching of alleles

Clonal & diploid models

Infinite loci, +/- alleles: Genetic polymorphism in each locus(Spichtig & Kawecki, in press)

Two loci, continuum of alleles: Initially both loci undergo branching, but only one remains polymorphic (Kisdi & Geritz 1999)

(d/)2 > 1/c1c2

A1A1 A1A2 A2A2

Habitat 1 1 1 - s/2 1 - s Habitat 2 1 - s 1 - s/2 1

Fixed alleles:

Hoekstra et al. 1985

Genetic Polymorphism

Protected polymorphism of similar alleles – under weak selection - ?!

+

+-

-

Evolving alleles:

Generic models of a wide class, both clonal and diploid:

no polymorphism of similar alleles away from singularities invasion implies fixation

near a singularity, protected polymorphism or rare disadvantageof similar alleles

fine-tuning done by directional evolution

if the singularity is an ESS, then the polymorphism is transienton the long-term evolutionary timescale

not every polymorphism is evolutionarily permanent

Genetic Polymorphism

Genetic Polymorphism

0

0.5

1

1 2 3 4d/

c1

evolutionarily stablepolymorphism (no branching)

evolutionary branching

Evolutionary branching is not necessary (neither sufficient) for evolutionarily stable polymorphism

Both clonal and diploid:

d/=3, c1=0.5

+

+

-

-

x1

x2

d/

Clonal model

After branching, two specialist phenotypes evolve

d/=2.25, c1=0.5

x1

x2

x1 x1

d/=3, c1=0.5 d/=5, c1=0.5

Diploid model

Will assortative mating restore the simplicity of the clonal model?

x1

x2

x1

x2

x1

x2

x1

x2

heterozygote inferiorityheterozygote inferiority

Evolution to strongest heterozygote inferiority

Time window for speciation

Assortative mating

"Two-allele mechanisms": (Felsenstein, 1981)strong selection is necessary to counterbalance recombination

Population Genetics of Assortative mating

Udovic (1980) model:

mating locus with two alleles (B, b)mating groups: BB+Bb and bb

p = penetrance: mating within group with prob. p,otherwise random mating

r = recombination between the ecological and the mating locus

In linkage equilibrium, alleles B and b are neutral

Ecological locus (no mutation):Mating locus: B, b

Gamete frequencies:)(

2)(

1)(

2)(

1 ,,, dB

dB

db

db QQQQ in the dominant (BB+Bb) mating group

)(2

)(1 , b

bbb QQ in the recessive (bb) mating group

Zygote frequencies:

jlikdd

jld

ikijkl qqpQQQpP )1(/ )()()(

)()()( , diBiB

dib

bibib QqQQq overall

jbibdd

jbd

ibbb

jbb

ibijbb qqpQQQQQQpP )1(// )()()()()()(

21 xx u = freq(x1) = 0.5v = freq(b)

Population Genetics of Assortative Mating

except

Zygote frequencies:

jlikdd

jld

ikijkl qqpQQQpP )1(/ )()()(

jbibdd

jbd

ibbb

jbb

ibijbb qqpQQQQQQpP )1(// )()()()()()(

Selection by the ecological locus:1 ),(1 ,1 xs relative fitnesses

Gamete frequencies by the standard Mendelian rules within each mating grouprecombination rate r

6 variables – 1 (sum of the Q's is 1) – 1 (symmetry, u=0.5)

Population Genetics of Assortative Mating

except

,,,, )(2

)(1

)(2

)(1

dB

dB

db

db QQQQ )(

2)(

1 , bb

bb QQ

Bistability of the gamete frequency dynamics:

v=freq(b)

D = qib - uv

critvv

critvv LE is stable

LE is unstable

p = 0.75r = 0.5s = 0.358(max s with d/=3, c1=0.5)

0

0.5

1

0 0.25

vcrit

Population Genetics of Assortative Mating

0

0.5

1

0 0.250

0.5

1

0 0.250

0.5

1

0 0.25

p = 0.85, r = 0.5 (Δx given for d/= 3, c1=0.5)

s=0.125 (Δx=1) s=0.194 (Δx=1.35) s=0.203 (Δx=1.4)

s=0.207 (Δx=1.42) s=0.239 (Δx=1.6) s=0.339 (Δx=2.4)

0

0.5

1

0 0.25

vcrit

vcrit0

0.5

1

0 0.250

0.5

1

0 0.25

frequ

ency

of a

llele

b

linkage disequilibrium, D = qib - uv

Population Genetics of Assortative Mating

reco

mbi

natio

n (r

)

penetrance (p)

LD evolves LD evolves if v is high enoughLD does not evolve1s = 0.358 (maximum for d/=3, c1=0.5)

Population Genetics of Assortative Mating

p=0.9, r=0.5, d/=3, c1=0.5

x1

x2

Assortative mating during branching

LE onlyLD + LELD only

Switch from LE to LDsomewhere in the orange banddepending on the frequency of b

Adaptive dynamics of alleles at LD

p=0.9, r=0.5, d/=3, c1=0.5

x1

x2

d/ -0.2 0 0.2 0.4 0.6 0.8

heterozygote deficiencybefore / after selection

F

p=0.9, r=0.5, d/=3, c1=0.5

x1

x2

Assortative mating during branching

LE onlyLD + LELD only

Switch from LE to LDsomewhere in the orange banddepending on the frequency of b

LD exists LE only

Adaptive dynamics of alleles at LD

LD permanent – incipient speciation

LD lost

p=0.73, r=0.5, d/=3, c1=0.5

x1

x2

p=0.85, r=0.5, d/=3, c1=0.5

x1

x2

Prospects for speciation

reco

mbi

natio

n (r

)

penetrance (p)

Levene model with d/= 3, c1 = 0.5

Left to the red line: AD saddle LD does not evolve LD may evolve but will be lostRight to the red line: AD attractor LD evolves LD evolves if v is high enough

1

Prospects for speciation

B and b are neutral at LE

- mutational equilibrium- drift and hitchhiking: the frequency of allele b, v, is

most often near 0 (LD in ) or near 1 (LD in and ) - sexual selection: if rare males are at a disadvantage,

B or b will be rare and selected against

Increasing penetrance

- natural selection favours increased p at LD- increasing p transforms a saddle into an attractor of AD- closes gene flow down

- role of temporary LD in increasing penetrance

(Dieckmann and Doebeli 1999)

Prospects for speciation

"Byproduct" speciation

- no LD is needed between the ecological and mating loci

- sexual selection may counterbalance disruptive natural selection (Kirkpatrick and Nuismer 2004), and causes a bistability in the evolutionary dynamics of assortment (Matessi et al. 2001, Meszéna and Christiansen in prep.)

- environmental variance in the selected trait constrains the maximum attainable level of assortment

An Adaptive Dynamics Perspective

... on polymorphism

directional evolution takes care of "fine tuning"polymorphism may be transient in evolution(evolution near an ESS, evolution to extinction)evolutionary branching is neither necessary nor sufficientfor an evolutionarily stable polymorphism to exist

... on speciation

evolution can lead to strong disruptive selectionbut can lead away from it again (time window)competing processes: evolution of dominance,sexual dimorphism, mixed strategies

An Adaptive Dynamics Perspective

... on speciation

- evolution to polymorphism under disruptive selection appears to be common

- reproductive isolation: depends on genetics

Alliance with population genetics needed!